Expand and combine like terms. $(2a^6-6a^3)^2=$
Solution: We can expand this expression using the "perfect square" pattern (where $P$ and $Q$ can be any monomial): $(P+Q)^2=P^2+2PQ+Q^2$ Since we have a minus sign, let's rewrite the binomial as a sum where the second term is negative, then use the pattern. $\begin{aligned} &\phantom{=}\left(2a^6-6a^3\right)^2 \\\\ &=\left(2a^6+\left(-6a^3\right)\right)^2 \\\\ &=(2a^6)^2+2(2a^6)(-6a^3)+(-6a^3)^2 \\\\ &=4a^{12}-24a^9+36a^6 \end{aligned}$